4.) evalnate the integral dx aresinx a. WI-Y b) S x arctanx dx

Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: (a) Use the trapezoidal rule to approximate the integral. dx

A: Solution of given question is written in below steps.

Q: Evaluate the triple iterated integral. xyz³ dx dy dz

A: ∫02∫02∫-14xyz3dxdydz=∫02∫02x2yz32x=-1x=4dydz…

Q: Integration in REVERSE ORDER

A: Given:

Q: Calculate the iterated integral. 7. 2xex dy dx Jo

A:

Q: 1- Use trapezium's Rule with n = 4 to approximate the integral Vx dx

A: We have to use formula of Trapezoid Rule.

Q: 3 Estimate the integral 1 dx by the trapezoidal rule using n = 4. + 1 Vx3

A: ∫abf(x)dx≈Δx(f(x0)+f(x1)2+f(x1)+f(x2)2+f(x2)+f(x3)2+⋯+ f(xn−1)+f(xn)2) where ∆x =b -an

Q: Show that ∫0∞ e-x 2 dx = ∫10√(-ln y)  dy  by interpreting theintegrals as areas.

A:

Q: b) Estimate the integral esindx using composite traperoidal rule with h= 0.25.

A:

Q: Evaluate the integral. arctan dx 1

A: For evaluating the given integral, we will use the concepts of integral by parts and integration…

Q: Evaluate iterated integral.

A: Given, ∫01 ∫36 xx2+3y dx dy

Q: Use (a) the Trapezoidal Rule integral 1to 4    cos  2  x dx                 with n= 8

A: Given Data The integral is . The number of intervals is n=8.   The function of the given integral…

Q: Evaluate the integral / (2x + 9y)dx + (6x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

A:

Q: Evaluate the integral arc y = x² from (0,0) to (1,1). NOTE: Enter the exact answer. (2x + 18y)dx +…

A: Given integral is ∫C(2x+18y)dx +(3x-y)dy We have to evaluate given integral along a parabolic arc…

Q: Evaluate the double integral : dy dz

A:

Q: Evaluate iterated integral.

A: Let the given integral be I - I = ∫39∫57 xy+y5dx dy  Let's first integrate with respect to x (we…

Q: Calculate $o (3x + 5y - cos(y)) dx + x sin(y) dy if C encloses a region of area 4.

A: To evaluate the given integral.

Q: aluate the iterated integral. || 5x²sin(y) dy dz dx =

A: Given: ∫0π∫05x∫0xz5x2sinydydzdx

Q: Use the 4_segment trapezoidal Rule to numerically integrate. S(0.2 + 25x + 3x²) dx

A:

Q: Evaluate the iterated integral.

A: The given integral is ∫01∫0y6x+5y3dxdy

Q: Find the approximation of the integral. 1= [e*dx Using Romberg's rule derived from Trapezoidal rule…

A: Given integral I=∫01e-x2dx Here we use Romberg's rule derived from Trapezoidal rule for 1,2,4,8…

Q: Evaluate the integral (12x + 15y)dx + (24x – y)dy along the paraboli arc y = x from (0,0) to (1,1).…

A:

Q: Please solve the given line integral which is the following: Se(x² + y²) dx – x dy In where C is the…

A: The given line integral is: L=∫Cx2+y2 dx -xdy where C is the arc of quarter circle that is going…

Q: Evaluate triple integral ſ´, S,2 ¯* dz dx dy .

A: We can solve this as follows:

Q: Calculate the integral approximations Tb and Mb for sec x dx %3D

A:

Q: Evaluate the iterated double integral: esec y+1 dy dx. VE sin y sec

A: To evaluate the iterated double integral :               ∫14∫sec-1xπ3  esecy+1sin ydydx

Q: Evaluate the iterated integral. dx dy

A: Given query is to find the indicated integral.

Q: Calculate the approximate to the integral -5 (24 +2x² − 3)dx, by the composite midpoint rule with…

A:

Q: Evaluate the triple iterated integral. 12 2 3. xyz dx dy dz

A: Given a function f(x,y,z)=xyz3 To find ∫02∫02∫-12xyz3dxdydz

Q: Use Simpson's Rule e with n=10 Y: X Sin (x), OSXS 27

A:

Q: Evaluate the integral. arctan(5t) dt

A: Here we evaluate the integral∫ arc tan 5t dt

Q: The improper integral fx dx is

A: An improper integral is the limit of a definite integral as an endpoint of the interval of…

Q: The suitable substitution to evaluate the integral (V cot (2x) dx is sin (2x) Ou3tan(2x) none Ou=…

A: To find The suitable substitution to evaluate the integral.

Q: 2.a) Apply the Trapezoid and corrected trapezoid rule, with h = 1, to approximate the integral 1 dx…

A:

Q: Determine the avarage Valve of + he Aunction fex)=Cas(z)-Sin Cx/2) PA L-2, by using The meen vaelve…

A:

Q: The integral that represents the arc-length of the curve y = In x, xE [2,3] is: %3D 3 x2+1 dx. Vx2+1…

A:

Q: Evaluate the integral. ∫arctan 4t dt

A:

Q: he integral dx こ [in(x)]? x[In(x

A: Given integral is ∫1x(1nx]2dx let’s find the value

Q: Evaluate the in tegral (x+ 2y) dy

A:

Q: Approximate the integral | dx using 4 trapezoids .2 1

A: Introduction: The formula for the trapezoidal rule is given by, ∫aby(x)dx=h2y0+yn+2(y1+y2+...+yn-1)

Q: Evaluate the iterated integral. 3 4ze dy dx dz

A:

Q: Q2: Evaluate the integral fx In x dx using by parts formula

A: Note:- As per our guidelines, We can answer the first question since the exact one wasn’t specified.…

Q: (5) Obtain the integral curve for dy +y cotx = e*cscx passing through the dx point (0, 0).

A: We have to solve the given differential equation

Q: Evaluate the triple iterated integral. xyz dx dy dz

A:

Q: dydx tan x 1. 1+ y²

A: We need to calculate double integral in given order dydx   we use result of inverse Trigonometry…